Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator.

DOI10.1007/S00220-013-1876-XzbMath1306.20007arXiv1209.4800OpenAlexW2022066163MaRDI QIDQ2450865

Anatoly M. Vershik, Natalia V. Tsilevich

Publication date: 23 May 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4800

zbMATH Keywords

tensor productsSchur-Weyl dualityGelfand-Tsetlin algebrasrepresentations of the infinite symmetric groupCoxeter-Laplace operator

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Applications of group representations to physics and other areas of science (20C35) Representations of infinite symmetric groups (20C32)

Related Items (5)

Criteria of irreducibility of the Koopman representations for the group \(\mathrm{GL}_0(2\infty,\mathbb R)\) ⋮ A new generalized Schur-Weyl duality ⋮ An analogue of Schur-Weyl duality for the unitary group of a $\mathrm{II}_1$-factor ⋮ Schur–Weyl quasi-duality and (co)triangular Hopf quasigroups ⋮ The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra \(\widehat{\mathfrak{sl}_2}\).

Cites Work

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• Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case
• Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum
• The representation theory of the symmetric groups
• On the behaviour of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits
• Tensor Representations of Classical Locally Finite Lie Algebras
• Markov Measures on Young Tableaux and Induced Representations of the Infinite Symmetric Group

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